摘要
A black ring is an asymptotically fiat vacuum solution of the n-dimensional Einstein equations with an event horizon of topology S1× Sn-3. In this study, a connection between the black ring entropy and the Weyl tensor Cμνλρ is explored by interpreting the Weyl scalar invariant CμνλρCμνλρ as the entropy density in five-dimensional space-time. It is shown that the proper volume integral of CμνλρCμνλρfor a neutral black ring is proportional to the black ring entropy in the thin-ring limit. Similar calculations are extended to more general cases： a black string, a black ring with two angular momenta, and a black ring with a cosmological constant. The proportionality is also found to be valid for these complex black objects at the leading order.
A black ring is an asymptotically fiat vacuum solution of the n-dimensional Einstein equations with an event horizon of topology S1× Sn-3. In this study, a connection between the black ring entropy and the Weyl tensor Cμνλρ is explored by interpreting the Weyl scalar invariant CμνλρCμνλρ as the entropy density in five-dimensional space-time. It is shown that the proper volume integral of CμνλρCμνλρfor a neutral black ring is proportional to the black ring entropy in the thin-ring limit. Similar calculations are extended to more general cases： a black string, a black ring with two angular momenta, and a black ring with a cosmological constant. The proportionality is also found to be valid for these complex black objects at the leading order.
